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Search: id:A115627
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| A115627 |
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Multiplicity of p_k as a divisor of n!. |
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3
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| 1, 1, 1, 3, 1, 3, 1, 1, 4, 2, 1, 4, 2, 1, 1, 7, 2, 1, 1, 7, 4, 1, 1, 8, 4, 2, 1, 8, 4, 2, 1, 1, 10, 5, 2, 1, 1, 10, 5, 2, 1, 1, 1, 11, 5, 2, 2, 1, 1, 11, 6, 3, 2, 1, 1, 15, 6, 3, 2, 1, 1, 15, 6, 3, 2, 1, 1, 1, 16, 8, 3, 2, 1, 1, 1, 16, 8, 3, 2, 1, 1, 1, 1, 18, 8, 4, 2, 1, 1, 1, 1, 18, 9, 4, 3, 1, 1, 1, 1, 19, 9
(list; graph; listen)
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OFFSET
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2,4
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COMMENT
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Factorization of n!; n! = 2^T(n,1)*3^T(n,2)*...*P_{Pi(n)}^T(n,Pi(n)).
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FORMULA
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T(n, k) = Sum_{i=1}^{inf} [n/p_k^i]. (Although stated as an infinite sum, only finitely many terms are nonzero.)
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EXAMPLE
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Rows start: 1; 1,1; 3,1; 3,1,1; 4,2,1; 4,2,1,1; 7,2,1,1; 7,4,1,1.
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CROSSREFS
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Cf. A090622, A090623, A000142, A115628. Row lengths are A000720. Columns include A011371, A054861, A027868, A054896, A090617, A064458, A090620.
Sequence in context: A066975 A098877 A091088 this_sequence A128218 A010283 A134699
Adjacent sequences: A115624 A115625 A115626 this_sequence A115628 A115629 A115630
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KEYWORD
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nonn,tabf
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 26 2006
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